Some existing systems for ground positioning are based on GPS. GPS includes twenty-four active satellites orbiting the earth that were put in place by the United States Department of Defense. Each satellite continuously broadcasts a signal that contains an L-band carrier component (L1), which is transmitted at a frequency of 1.575 GHz. The L1 carrier component is modulated by a coarse acquisition (C/A) pseudo random (PRN) code component and a data component. The PRN code provides timing information that allows determination of when the GPS signal was broadcast. The data component provides certain GPS information, such as the satellite's orbital position.
Existing methods for position determination include Conventional GPS, in which a receiver makes ranging measurements between an antenna coupled to the receiver and each of at least four GPS satellites in view. The receiver makes these measurements from the timing information and the satellite orbital position information obtained from received GPS signal information. By receiving four different GPS signals, the receiver can make position determinations. However, the accuracy of Conventional GPS is only to within tens of meters of actual position. This accuracy is generally not sufficient for controlling land vehicles.
A more accurate use of GPS is Ordinary Differential GPS, in which position determination is made using similar ranging measurements to those made with Conventional GPS. However, a ground reference receiver at a precisely known location is utilized to increase accuracy. The method depends on the assumption that satellite ranging errors can be expected to affect position determinations made by the user's receiver in the same way as they will the position determinations for the reference receiver. Since the precise location of the reference receiver is known, its calculated position determination can be compared to the actual position to determine the ranging error, which is then used to compute suitable corrections for the user's receiver. The user then applies the corrections to the user's location determinations.
Additional corrections using Ordinary Differential GPS can be made using a ground-based pseudo satellite ("pseudolite") and an unassigned PRN code, which allows the user's receiver to make a redundant fifth ranging determination for greater accuracy. These methods allow accuracy of position determination to several meters.
Meter-level code-differential GPS techniques are currently used for mapping and yield monitoring (see for example, G. Lachapelle, et al., GPS Systems Integration and Field Approaches in Precision Farming, 41 Navigation 323-335 (Fall 1994); J. Pointon and K. Babu, LANDNAV: A Highly Accurate Land Navigation System for Agricultural Applications, Proceedings of ION GPS-94, Salt Lake City, Utah, 1077-1080 (September, 1994); Kurt Lawton, GPS System in a Box, Farm Industry News 10 (July/August 1995)), and the use of GPS in relation to field topographic mapping has been explored (see, for example, R. L. Clark and R. Lee, A Comparison of Rapid GPS Techniques for Development of Topographic Maps for Precision Farming, Proceedings of ION GPS-96, Kansas City, Mo., 495-504 (September 1996)). A low-cost, real-time precision navigation system has numerous potential applications in land vehicles such as data collection, driver guidance, and automatic control.
One accurate technique for position determination known in the art is Carrier Phase Differential GPS (CDGPS). CDGPS utilizes the 1.575 GHz carrier component of the GPS signal and superimposition of the PRN code and data component. The method typically involves generating position determinations based on the measured phase differences between two different antennas for the carrier component of a GPS signal. This technique requires initial determination of how many integer wavelengths of the carrier component exist between the two antennas at a particular point in time, a method referred to as integer ambiguity resolution.
CDGPS offers the potential for low-cost precision navigation that does not require specific external cues for successful operation. Robot vehicles using this technology may someday be used to clear minefields, clean up toxic waste, apply hazardous pesticides, tirelessly harvest crops, and transport disabled people. The first widespread use of CDGPS in land vehicles will most likely occur in farm equipment. Fields typically have good sky visibility, making them highly suitable for GPS. Also, the cost versus production rewards to be gained through precision farming are significant (see, for example, R. J. Palmer and S. K. Matheson, Impact of Navigation on Farming, International Winter Meeting of the American Society of Agricultural Engineers, Chicago, Ill. (December 1988)).
In determining position using CDGPS, integer search techniques are typically used to measure residuals to find the correct integers, a technique prone to false solutions. Such a loss of system integrity could be costly or even dangerous in many high accuracy GPS applications. A successful method that is known in the art is use of a motion-based method that has been applied to static surveying applications. This approach involves taking a number of phase measurements while the user's antenna and a reference antenna are stationary. These phase measurements are typically made over a period from 15 minutes to 90 minutes. The phase measurements made during the slowly changing geometry of the GPS satellites reveal the integer ambiguities.
A motion-based method used for aircraft involves use of four antennas--one on the tail, one on the fuselage, and one on each wing tip. Using the fuselage antenna as a reference antenna, integer ambiguities may be resolved in seconds by rotating the aircraft and taking several phase measurements. However, because the reference antenna and the other antennas are fixed to the aircraft, this method, while useful for precise attitude determinations for the aircraft, is not useful for precise position determination. Moreover, it is not believed to have been adapted for use in connection with automatically controlling movement of a land vehicle.
Another currently available initialization technique, which was created for precision aircraft landing, reduces the fundamental limitations of the above methods but requires use of two or more GPS pseudo-satellite transmitters for CDGPS initialization. By providing additional ranging signals, the use of pseudolites improves GPS system availability and integrity (see, for example, B. S. Pervan, et al., Integrity Monitoring for Precision Approach Using Kinematic GPS and a Ground-Based Pseudolite, 41 Navigation 159-174 (Summer 1994)). This is especially important when obstructions or excessive vehicle attitude motion may result in the loss of GPS satellite signals.
A minimum of two pseudolites are needed for the aircraft landing system, a system referred to as the Integrity Beacon Landing System (IBLS) (see, for example, C. E. Cohen, et al., Real-Time Flight Testing Using Integrity Beacons for GPS Category III Precision Landing, 41 Navigation 145-157 (Summer 1994)). For a straight trajectory, it can be shown that each pseudolite provides an accurate measurement of along-track and radial position, but no information about cross-track position (see, for example, C. E. Cohen, et al., Real-Time Cycle Ambiguity Resolution Using a Pseudolite for Precision Landing of Aircraft with GPS, Second International Symposium on Differential Satellite Navigation Systems, Amsterdam, The Netherlands (March 1993)). This problem is solved by placing two pseudolites on opposite sides of the approach path. These pseudolites complement each other to produce a highly accurate and robust three dimensional navigation solution.
A method for use with aircraft positioning determination involving use of one or more pseudolites is described by U.S. Pat. No. 5,572,218 issued to Clark Cohen et al., System and Method for Generating Precise Position Determinations. The system comprises a ground-based stationary reference GPS system and a mobile GPS system mounted on a moving vehicle. The stationary reference station includes a GPS reference receiver, an initialization pseudolite, a data link pseudolite, and a reference antenna.
The data link pseudolite generates and broadcasts a signal beam data link signal, which has at least a carrier component and a data component. The initialization pseudolite generates and broadcasts a low power signal bubble initialization signal, which has at least a carrier component. The reference antenna receives GPS signals broadcast by GPS satellites and provides them to the reference receiver. The reference receiver determines phase measurements at periodic measurement epochs for the carrier phase components of the GPS signals and may also conduct these measurements for the carrier component of the initialization signal. Data regarding these phase measurements is received by the data link pseudolite and then transmitted to the mobile system via the data component of the data link signal.
The mobile elements of this system comprise a GPS position receiver and two antennas. One antenna receives the same GPS signals as received by the reference antenna, both during and after an initialization period. The second antenna receives the initialization and data link signals form the two pseudolites during the initialization period and then continues to receive only the data link signal after that period. Each of the GPS signals received by the first antenna and the reference antenna has an integer ambiguity associated with these two antennas. The initialization period is used to resolve these integer ambiguities so that the mobile GPS position receiver can generate precise position determinations for the first antenna using CDGPS.
During initialization, the GPS position receiver receives the GPS signals and the initialization and data link signals from the two antennas. The vehicle moves about during this period within the signal bubble, and a large angular change in geometry results between the moving vehicle and the initialization pseudolite. The mobile GPS position receiver makes and records phase measurements for the GPS signals and the initialization signal over the large change in geometry. These phase measurements are made during the same epochs as those made by the GPS reference receiver over this same change in geometry. In addition, the mobile GPS receiver receives via the data link signal the phase measurements made by the GPS reference receiver and records them. From the recorded phase measurements of both receivers, the GPS position receiver can accurately compute initialization values representing resolutions of the integer ambiguities of the GPS signals. Thus, the large angular change in geometry reveals the integer ambiguities.
Once these initialization values have been computed, the initialization period is over and the moving vehicle will have left the signal bubble. The mobile GPS receiver can then compute precise positions for the first antenna at each measurement epoch to within centimeters of the exact location. This is done using the computed initialization values, the phase measurement for the GPS signals made by the mobile position receiver, and the phase measurements made by the GPS reference receiver provided to the GPS position receiver via the data link signal.
In determining positioning using CDGPS and a single pseudolite for a vehicle such as a land vehicle, a series of equations may be used and manipulated. The non-linear equation for a differential carrier phase measurement of pseudolite j at epoch k is (see B. Pervan, Navigation Integrity for Aircraft Precision Approach using the Global Positioning System): EQU .phi..sub.jk =.vertline.p.sub.j -x.sub.k .vertline.+.tau..sub.k +N.sub.j +.nu..sub.jk
where:
.phi..sub.jk =Raw single difference carrier phase measurement PA1 p.sub.j =Position of pseudolite j PA1 x.sub.k =Vehicle antenna position PA1 .tau..sub.k =Clock bias PA1 N.sub.j =Cycle ambiguity for pseudolite j PA1 .nu..sub.jk =Measurement noise with standard deviation .sigma..sub..PHI. PA1 i=2 . . . m EQU .delta..phi..sub.jk =-e.sub.jk T.delta.x.sub.k +.tau.'.sub.k +N'.sub.j +.nu..sub.jk, PA1 i=1 . . . n PA1 e.sub.ik =Line-of-sight unit vector to satellite i PA1 e.sub.jk =Estimated line-of-sight unit vector to pseudolite j PA1 .tau.'.sub.k =Clock bias+cycle ambiguity for satellite 1 PA1 N'.sub.i =Cycle ambiguity for satellite i-satellite 1
This equation can be linearized about an estimate of vehicle position and combined with the satellite differential carrier phase equations. The basic linearized carrier phase measurement equations for m satellites and n pseudolites at epoch k can then be written as follows (see, for example, B. Pervan, Navigation Integrity for Aircraft Precision Approach using the Global Positioning System, Ph.D. Dissertation, Stanford University, SUDAAR 677 (March 1996)): EQU .delta..phi..sub.lk =-e.sub.lk T.delta.x.sub.k +.tau.'.sub.k +.nu..sub.lk EQU .delta..phi..sub.ik =-e.sub.ik T.delta.x.sub.k +.tau.'.sub.k +N'.sub.i +.nu..sub.ik,
where:
For a single epoch, there are more equations (m+n), than unknowns (m+n+3), so there is no explicit solution for this set of equations. If a wide range of integer cycle ambiguity candidates are substituted into these equations, the set producing the lowest mean-square residual is often (but not always) the correct integer solution.
As additional epochs of data are collected, the integer cycle ambiguities do not change. Each new epoch of data produces m+n more equations and only four more unknowns (.delta.x.sub.k and t'.sub.k). A sufficient geometry change is needed to resolve the integer ambiguities. For an aircraft on a straight flight path, four satellites and two pseudolites are needed to provide "geometric leverage" to resolve the ambiguities.
Experimental work regarding use CDGPS for control of a land vehicle (a golf cart) is described in Michael O'Connor, et al., Kinematic GPS for Closed-Loop Control of Farm and Construction Vehicles, ION GPS-95, Palm Springs, Calif. (September 1995). The system described in this article utilized a GPS receiver to produce carrier phase measurements for attitude determination and a separate receiver to determine vehicle position. An on-board computer performed attitude, position, and control signal computations. In addition to the vehicle, the system included a ground reference station consisting of a computer and a GPS receiver used to generate carrier phase measurements and code differential corrections. The data from the reference station was transmitted to the vehicle via a radio modem.
The results described in the above-referenced O'Connor article showed that more control effort was required, and accuracy was poorer than predicted by simulation. This was most likely due to an inexact disturbance model in the simulation. One likely cause of the disturbance noise was the roll motion of the vehicle (a golf cart). Although the roll angle of the vehicle was measured, the resulting motion of the two meter high positioning antenna relative to the wheel base was not corrected for by this system. Thus, the technique described in this article includes no control correction for such effects as vehicle roll due to ground disturbances. Failure to measure a vehicle's roll is a significant hindrance to effective control on non-smooth surfaces.